The analogy is only there to point out the flaw in your thinking, the lack of persistence applies to both humans (if we shoot them quickly) and LLMs and so your argument applies in both cases. And I can do the very same trick to the clock analogy. You want to say that a clock is designed to keep time and that's all it does therefore it can't understand time. But I say, look, the clock was designed to keep time yes but that is far from all it does, it also transforms electrical energy into mechanical and uses it to swing around some arms at constant speed, and we can't see the inside of the clock who knows what is going on in there, probably nothing that understands the concept of time but we'd have to look inside and see. LLMs were designed to predict the next token, they do actually do so, but clearly they can do more than that, for example they can solve high school level math problems they have never seen before and they can classify emails as being spam or not. Yes these are side effects of their ability to predict token sequences as human reasoning is a side effect of their ability to have lots of children. The essence of a task is not necessarily the essence of the tool designed specifically for that task.
If you believe LLMs are not complex enough to have understanding and you say that head on I won't argue with you, but you're claiming that their architecture doesn't allow it even in theory then we have a very fundamental disagreement